Slantlet Transform for Multispectral Image Fusion

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Journal of Computer Science 5 (4): 263-269, 2009 ISSN 1549-3636 © 2009 Science Publications Slantlet Transform for Multispectral Image Fusion 1 Adnan Hadi M. Al-Helali, 1Hamza A. Ali, 1Buthainah Al-Dulaimi, 1 Dhia Alzubaydi and 2Walid A. Mahmmoud 1 Faculty of Computer Science and Information Technology, 2 Faculty of Engineering, Al-Isra Private University, P.O. Box 22, Post Code: 11622, Amman, Jordan Abstract: Problem statement: Image fusion is a process by which multispectral and panchromatic images, or some of their features, are combined together to form a high spatial/high spectral resolutions image. The successful fusion of images acquired from different modalities or instruments is a great importance issue in remote sensing applications. Approach: A new method of image fusion was introduced. It was based on a hybrid transform, which is an extension of Ridgelet transform. It used the slantlet transform instead of wavelet transform in the final steps of Ridgelet transform. The slantlet transform was an orthogonal discrete wavelet transform with two zero moments and with improved time localization. Results: Since edges and noise played fundamental role in image understanding, this hybrid transform was proved to be good way to enhance the edges and reduce the noise. Conclusion: The proposed method of fusion presented richer information in spatial and spectral domains simultaneously as well as it had reached an optimum fusion result. Key words: Fusion, multispectral, panchromatic, remote sensing, wavelet, transform, slantlet, image INTRODUCTION methods. The spatial information of fused image is an important factor as much as the spectral information in many remote sensing applications. In particular, this improves the efficiency of the image fusion application, such as unsupervised image classification. In other words, it is necessary to develop advanced image fusion method so that the fused images have the same spectral resolution as the multispectral images and the same spatial resolution as the panchromatic image with minimum artifacts Choi et al.[4]. In this study, firstly, a new Hybrid transform which is improvement from the Ridgelet transform is proposed. The Hybrid transform is based on replacing the Wavelet transform in the Ridgelet transform with the Slantlet transform. This method provides richer information in the spatial domains than Wavelets by represents better edges since edges play a fundamental rule in image understanding. A good way to enhance spatial resolution is to enhance the edges. Theoretical basis of the Hybrid transform is described next. Then, the new image fusion approach for panchromatic and multispectral images based on the Hybrid transform is presented, followed by discussion of the image fusing experiments. Next, the experimental results are analyzed. Remote sensing and mapping are some of the application fields benefiting from the image fusion. Many image fusion techniques and software tools have been developed. The well-known methods are, for example, Principle Component Analyses (PCA) introduced by Chavez[1], Intensity Hue Saturation (IHS) transform performed by de Bethune et al.[2] and Brovey method proposed by Seetha et al.[3]. If the objective of image fusion is to construct synthetic images that are closer to the reality they represent, then, according to the criteria proposed by PCA, IHS and Brovey fusion methods meet this objective. However, one drawback of such methods is some distortion of spectral characteristics in the original multispectral images Choi et al.[4]. Recently, developments in wavelet analysis provide a potential solution to these drawbacks. Several wavelet based techniques for fusion of 2-D images have been described in the literature[4-17]. Wavelet-based image fusion method provides high spectral quality of the fused satellite images. However, the fused images by Wavelets have much less spatial information than those by the PCA, IHS and Brovey Corresponding author: Hamza A.Ali, Faculty of Computer Science and Information Technology, Al-Isra Private University, P.O. Box 22, Code: 11622, Amman, Jordan 263 J. Computer Sci., 5 (4): 263-269, 2009 Fig. 1: Hybrid Transform Structure The hybrid transform: To improve the performance of the individual transforms and to overcome their weakness points, here another transform is proposed, which is named as Hybrid transform. The main idea behind the Hybrid transform is, first to apply the two dimensions Fast Fourier Transform (2-D FFT) to the two dimensions signal (image). Next, to map line sampling scheme into a point sampling scheme using the Radon transform. It is required to take the one dimension inverse Fast Fourier Transform (1-D IFFT) for each column of the produced two dimensions signal. Finally, it is required to perform the Slantlet transform to each row of the resultant two dimensions signal. It is expected that this new hybrid transform will give a high performance and strong properties. This is because combines together the good properties of the local transforms. Particularly the Slantlet transform, the properties and performance of the Slantlet are higher even than that of the Wavelet transform. The structure of the Hybrid transform is given in Fig. 1. Fig. 2: Two-scale iterated filter bank and an equivalent structure MATERIALS AND METHODS Slantlet transform filter bank: The Slantlet uses a special case of a class of bases described by[18], the construction of which relies on Gram-Schmidt orthogonalization. It is useful to consider first the usual two-scale iterated DWT filter bank and an equivalent form, which is shown in Fig. 2. The “slantlet” filter bank described here is based on the second structure, but it will be occupied by different filters that are not products. With the extra degrees of freedom obtained by giving up the product form, it is possible to design filters of shorter length while satisfying orthogonality and zero moment conditions[19]. For the two-channel case, the shortest filters for which the filter bank is orthogonal and has K zero moments are the well known filters described by Daubechies[20]. For K = 2 zero moments the iterated Fig. 3: Two-scale filter bank structure using the slantlet filters of Fig. 2b are of lengths 10 and 4 but the slantlet filter bank with K = 2 zero moments shown in Fig. 3 has filter lengths of 8 and 4. Thus the two-scale slantlet filter bank has a filter length which is two samples less than that of a two-scale iterated Daubechies-2 filter bank. This difference grows with the number of stages. Some characteristic features of the Slantlet filter bank are orthogonal, having two zero moments and has octave-band characteristic. Each filter bank has a scale dilation factor of two and provides a multi-resolution decomposition. The slantlet filters are piecewise linear. Even though there is no tree structure for Slantlet it can 264 J. Computer Sci., 5 (4): 263-269, 2009 be efficiently implemented like an iterated DWT filter bank[21]. Therefore, computational complexities of the Slantlet are of the same order as that of the DWT. The filter coefficients used in the slantlet filter bank as derived in by Selesnick[21] are: E 0 (z) = (− 10 2 3 10 2 −1 − + )+( )z 20 4 20 4 + (− (1) 3 10 2 −2 10 2 −3 − )z + ( + )z 20 4 20 4 7 5 3 55 5 55 −1 − − ) + (− )z 80 80 80 80 9 5 55 −2 17 5 3 55 −3 )z + (− )z + (− + + 80 80 80 80 17 5 3 55 −4 9 5 55 −5 + (− − + )z + ( )z 80 80 80 80 5 55 −6 7 5 3 55 −7 + (− − − )z + (− )z 80 80 80 80 E1 (z) = ( 1 11 3 11 −1 )+( + )z + 16 16 16 16 5 11 −2 7 11 )z + ( + )z −3 +( + 16 16 16 16 7 11 −4 5 11 −5 )z + ( − )z +( − 16 16 16 16 3 11 −6 1 11 −7 )z + ( − )z + (− − 16 16 16 16 1 E 3 (z) = z −3E 2 ( ) z Fig. 4: Block diagram of image fusion based on hybrid transform (2) Step 3: Fusion selection step: There are three developed fusion rule schemes that can be used here for the proposed image fusion. The maximum selection scheme just picks the coefficient in each subband with the largest magnitude. The weighted average scheme developed by Kolczynski[22] uses a normalized correlation between the two images' subbands over a small local area. The resultant coefficient for reconstruction is calculated from this measure via a weighted average of the two images' coefficients. Finally, the window based verification scheme that developed by[7] creates a binary decision map to choose between each pair of coefficients using a majority filter. Since the proposed method of fusion uses the onedimension multiwavelet then there will be two bands rather than four bands which are low band (L) and the high band (H). Several experimental tests were carried out to test the fusion using the above three type schemes. It was found that using the weighted average is the best for fusion of the low band and the maximum selection scheme is the best among them for the band (H). E1 (z) = ( (3) (4) The proposed method of fusion consists of processing of the two images using the Hybrid transform as shown in Fig. 4. The two images are of the same scene, each with a different camera resolution. Usually the coefficients of each transform have different magnitudes within the regions of different resolution. The steps of image fusion using Hybrid Transform are: Step 4: Reconstruction or inverse Hybrid transform: The selection coefficients are reconstructed to get the new Intensity component for multispectral image by the Inverse Hybrid Transform. Step 1: Image conversion: Convert the multispectral image (RGB) to IHS space. The multispectral image converted from RGB (Red, Green and Blue) space to IHS (Intensity, Hue and Saturation). Step 5: Inverse (IHS) to (RGB) image: Finally, we convert the new Intensity component with the same H and S to the RGB component which represent the new multispectral image. The block diagram of the proposed image fusion is shown in Fig. 4. Step 2: Transform computation: Computation of slantlet transform of the two images. In this step the two images (the Pan Image and Intensity component of the RGB image) are decomposed using the Hybrid transform. RESULTS The IKONOS Panchromatic (1 m spatial resolution) and multispectral image (4 m spatial resolution) of a suburban area are shown in Fig. 5a and b respectively. 265 J. Computer Sci., 5 (4): 263-269, 2009 (a) (b) (c) (d) (e) (f) (a) (b) Fig. 5: IKONOS Panchromatic image and Multispectral image (×4 zoom). (a): PAN image; (b): MS image Different fusion methods applied to this data set to produce the fused multispectral images in Fig. 6. Since the Hybrid transform is well-adapted to represent pan image containing edges and the multiwavelet transform preserves spectral information of original multispectral images, the fused image has high spatial and spectral resolution simultaneously. From the fused image in Fig. 6, it should be noted that both the spatial and the spectral resolutions have been enhanced, in comparison to the original images. The spectral information in the original panchromatic image has been increased and the structural information in the original multispectral images has also been enriched. Hence, the fused image contains both the structural details of the higher spatial resolution panchromatic image and the rich spectral information from the multispectral images. Compared with the fused result by the wavelet, the fused result by the Hybrid has a better visual effect in IKONOS image fusion in Fig. 6. Assessing image fusion performance in a real application is a complicated issue. In particular, objective quality measures of image fusion have not received much attention. Some techniques to blindly estimate image quality are used in this research. Such quality measures are used to guide the fusion and improve the fusion performance. (g) Fig. 6: PCA, Brovey, WLT, DRGT and HYBRID fused Images. (a): Fused IHS image; (b): Fused brovey image; (c): Fused DWT based (haar) Image; (d): Fused DWT based (Db4) Image; (f): Fused DRGT based (haar) image; (g): Fused DRGT based (Db4) Image; (h): Fused hybrid image DISCUSSION The root mean square error: The Root Mean Square Error (RMSE) is found by tacking the square root of the 266 J. Computer Sci., 5 (4): 263-269, 2009 Table 1: Training and testing times for the network error squared divided by the total number of pixels in the image: RMSE = 1 N N ∑∑[I(r,c) − F(r,c)]2 N 2 r =1 c =1 Fusion method (Ideal value) HIS method Brovery method DWT based (haar) DWT based (Db4) DRGT based (haar) DRGT based (Db4) Hybrid method (5) Where: I (r, c) = the ideal image F (r, c) = the fused image N×N = the image size. This measure is used in Carter[3] The experimental result was analyzed based on the root mean square error (RMSE) in (Table 1): Fusion method (Ideal value) HIS method Brovery method DWT based (haar) DWT based (Db4) DRGT based (haar) DRGT based (Db4) Hybrid method Correlation coefficient: The closeness between two images can be quantified in terms of the correlation function. The correlation coefficient ranges from -1 to +1 Carter[3]. The correlation coefficient is computed from: N Corr(I,F) = N r =1 c =1 ( ) ( ) 2  N N 2  N N  ∑∑ I(r,c) − I  ∑∑ F(r,c) − F   r =1 c =1  r =1 c =1  Where: I (r, c) = The ideal image F(r, c) = The fused image Iand F = Stand for the mean corresponding data set N×N = The image size (6) B and new B (0) 43.61 39.04 PAN and new R (41.62) 11.18 14.70 PAN and new G (42.83) 3.63 6.56 PAN and new B (48.97) 10.97 15.20 26.81 26.81 26.81 70.66 73.50 78.20 26.74 26.74 26.74 25.61 25.56 31.45 24.67 2467 24.67 23.72 23.63 29.89 24.21 24.21 24.21 23.49 23.40 29.74 21.86 21.86 21.86 21.31 21.19 27.98 R and new R (0) 0.7205 0.6871 G and new G (0) 0.6944 0.6720 B and new B (0) 0.6798 0.7351 PAN and new R (41.62) 0.9858 0.9767 PAN and new G (42.83) 0.9975 0.9920 PAN and new B (48.97) 0.9877 0.9750 0.8871 0.8766 0.8727 0.8695 0.8758 0.8493 0.8877 0.8772 0.8733 0.8705 0.8763 0.8492 0.9063 0.8975 0.8947 0.8865 0.8946 0.8682 0.9101 0.9018 0.8991 0.8884 0.8968 0.8704 0.9309 0.9246 0.9233 0.9058 0.9165 0.8907 The correlation coefficient values between each new image band with the original panchromatic image indicate that the Hybrid fused method produces the closest correlation with the panchromatic bands compared to IHS, Brovey, DWT and DRGT methods Based on the experimental results obtained from this study, the Hybrid-based image fusion method is very efficient for fusing IKONOS images. Thus, this new method has reached an optimum fusion result CONCLUSION values of This study presented a newly developed method based on the Hybrid transform for fusing IKONOS images. The experimental study was conducted by applying the proposed method and compared with other image fusion methods, namely IHS, Brovey, wavelet and Ridgelet transform methods. Based on the experimental results using the RMSE and the correlation coefficient, the proposed method provides a good result, both visually and quantitatively, for remote sensing fusion. This due to the properties of the Hybrid transform in providing the alleviation of the the Table 2 shows that: G and new G (0) 43.61 45.42 Table 2: Training and testing times for the network The RMSE values between the fused image bands with their corresponding MS image bands indicate that the pixel values are less distorted in the, Hybrid method compared to the IHS, Brovey, DWT and DRGT methods The RMSE values between the fused images bands with the original PAN image indicate that the pixel values are less distorted in the Hybrid method compared to DWT based fusion. But it's more distorted compared to HIS, Brovey, DWT and DRGT methods ∑∑ ( I(r,c) − I )( F(r,c) − F ) R and new R (0) 43.61 47.05 The correlation coefficient values between each new image band with its original MS band indicate that the Hybrid fusion method produce the best correlation result 267 J. Computer Sci., 5 (4): 263-269, 2009 noise resulting from the fusion process due to the use of the Slantlet is well representing images containing edges. 9. REFERENCE 1. Chavez, P.S. Jr. and A.Y. Kwarteng, 1989. Extracting spectral contrast in Landsat thematic mapper image data using selective principal component analysis. Photogrammet. Eng. Remote Sens., 55: 339-348. 2. de Bethune, S., F. Muller and J.P. Donnay, 1998. Fusion of multispectral and panchromatic image by local mean and variance matching filter techniques. Fusion of Earth Data, Sophia Antipolis, Jan. 28-30, Nice, France, pp: 31-37. 10. 3. 4. 5. 6. 7. 8. 11. 12. Seetha, M., I.V. MuraliKrishna and B.L. Deekshatulu, 2005. Data fusion performance analysis based on conventional and wavelet transform techniques. Proceeding of the IEEE International Symposium on Geoscience and Remote Sensing, July 25-29, IEEE Xplore Press, USA., pp: 2842-2845. 1525660.pdf Choi, M., R.Y. Kim and M.G. Kim, 2004. The curvelet transform for image fusion. Int. Soc. Photogrammet. Remote Sens., 35: 59-64. 931.pdf Koren, I., A. Laine and F. Taylor, 1995. Image fusion using steerable dyadic wavelet transforms. Proceedings of the IEEE International Conference on Image Processing, Oct. 23-26, IEEE Computer Society, Washington DC., USA., pp: 232-235. DOI: 10.1109/ICIP.1995.537623 Hill, P.R., D.R. Bul and C.N. Canagarajah, 2005. Image fusion using a new framework for complex wavelet transforms. Proceeding of the IEEE International Conference on Image Processing, ICIP, Sept. 11-14, IEEE Xplore Press, USA., pp: 1338-1341. DOI: 10.1109/ICIP.2005.1530311 Li, H., B.S. Manjunath and S.K. Mitra, 1995. Multisensor image fusion using the wavelet transforms. Graph. Models Image Process., 57: 235-245. DOI: there were some phenotype variations of Shh expression in the mutants. Some mutants showed the prominent reduction of its expression in the hindlimb bud (data not shown). In accordance with such variable expression pattern, digit phenotype was also variable (data not shown). In fact, several papers suggest various digit phenotypes in human patients of sirenomelia [44], [45]. The transcription factor Lmx1b is expressed in the dorsal mesenchyme of the limb bud and is a primary regulator of dorsal limb identity [46], [47]. Its expression was detected in the mesenchyme of mutant mice at the ventral caudal midline of the body (Fig. 7 H, yellow arrow and inset). These results suggest that the hindlimb patterning is basically maintained in Bmp4 cKO mice. Taken together, these results suggest early hindlimb bud grows out normally but rather the midline tissue is missing. Thus the hindlimbs may be fused and abnormally rotated. Abnormalities in the aPCM of Bmp4 cKO mice may lead to such loss of midline structure in the mutant mice subsequently leading to the approximation of hindlimb to the midline with change of the Lmx1b expression. Recent reports indicate that Tbx4 regulates the formation of hindlimb skeletal elements such as fibula [48], [49]. Expression of Tbx4 was reduced in Bmp4 cKO mice (Fig. 7 I, J). These results suggest a possibility that the defective patterning of Tbx4 expression may cause the abnormal fibula formation in the mutant embryos. Figure 2. Defective formation of the pelvic/urogenital organs in Bmp4 cKO mice. (A–F) Bmp4 cKO mice have bladder aplasia (red arrow in B) and hypoplastic kidney (yellow arrowheads in B), hypoplasia of external genitalia (arrow in D) and anal stenosis (arrowhead in F). red arrow, bladder; yellow arrowhead, kidney; arrow, genital tubercle; arrowhead, ano-rectal region. doi:10.1371/journal.pone.0043453.g002 urogenital organs has not been examined. Therefore, we analyzed the Isl1 conditional KO mice during caudal body formation. We utilized Hoxa3-Cre, which is expressed broadly in the caudal body region from E8.5 [31]. The mutant embryos showed hypoplastic aPCM and defective hindlimb initiation, but the expression of Gli1 and Bmp4 persisted in the aPCM (data not shown). Taken together, these results show that BMP4 signaling in the caudal Isl1 expression domains is required for the aPCM formation and loss of this signal (rather than decreased Isl1 function) causes the profound phenotypes of Isl1Cre;Bmp4flox/flox mutants. Functional redundancy of BMP genes has been shown in multiple developing organ systems [32–35]. Bmp4 cKO mice have both hindlimb fusion and defective pelvic/urogenital organs indicating that BMP4 is the critical ligand for caudal body development. Bmp7 KO mice do not show sirenomelia phenotypes (Fig. 6 B, F), but display kidney hypoplasia [20], [21]; implying possible functional redundancy of BMP signaling. Indeed, loss of a single copy of Bmp4 and both copies of Bmp7 in Bmp4flox/+Bmp7flox/flox compound mutant mice (Hoxa3Cre;Bmp4flox/+Bmp7flox/flox) resulted in hindlimb fusion (Fig. 6 D) as well as loss of the bladder and anal stenosis, essential diagnotic features of sirenomelia (n = 3) (Fig. 6 H). The same phenotypes were also observed in such double compound mutant mice. These results indicate that Bmp4 compensates for the loss of Bmp7 during caudal body development. PLOS ONE | Discussion Bmp4 cKO mice as mouse model of sirenomelia with hindlimb fusion and lethal pelvic/urogenital organ aplasia We have identified Bmp4 cKO mice as a new mouse model for sirenomelia. Unlike previous mouse models, the current model displays all the key phenotypes of sirenomelia including hindlimb fusion, dysgenesis of pelvic/urogenital organs and hypoplasia of external genitalia. The kidneys and upper urinary tract are retroperitoneal organs whereas the bladder and urethra are caudal intra-peritoneal organs derived from the cloaca. Our study has 4 September 2012 | Volume 7 | Issue 9 | e43453 A New Mouse Model of Sirenomelia Figure 3. Tissue contribution of Isl1-expressing cells to the caudal body. (A–H) Expression pattern of Isl1 mRNA during caudal body development. (A, E) Isl1 is expressed in the lateral plate mesoderm adjacent to the future hindlimb bud and the base of the allantois at E8.5 (bracket in A and E). (B, F) Isl1 is expressed in the caudal body region and hindlimb bud at E9.5 (square in B). Its expression is detected in the peri-cloacal regions (square in F). (C, G) Isl1 expression is detected in the cloacal region at E10.5 (arrow in C). It is expressed in the URS (arrowhead in G) and cloacal mesenchyme including aPCM (square in G). Isl1 expression in the hindlimb bud is reduced at E10.5. (D, H) Its expression is maintained in the developing GT at E11.5 (arrow in D). Its expression is detected in GT mesenchyme and URS (arrowhead in H). Asterisk indicates cloaca. (I–P) The R26RlacZ Cre reporter shows LacZ staining of caudal body regions in Isl1-mER-Cre-mER embryos at E15.5 after administration of tamoxifen at E8.5–E11.5. Whole-mount view of stained embryos of hindlimb and external genitalia (I–L) and pelvic organs (M–P). Isl1-expressing cells contribute to the hindlimb, external genitalia and bladder. Insets in I–L are high magnification of GT. Ventral GT is located at the bottom. t, tail; hl, hindlimb bud. doi:10.1371/journal.pone.0043453.g003 including pelvic/urogenital organs and hindlimb. We found Isl1expressing cells contribute to the aPCM formation. Tbx4 and Tbx5 are expressed in the aPCM region. Tbx4 is expressed in the umbilical cord, aPCM and also hindlimb bud. On the other hand, Tbx5 is not expressed in the hindlimb bud and its expression is more restricted in the aPCM. Thus, Tbx5 would be a one of the appropriate markers for the aPCM. Bmp4 cKO mice show defective tissue formation such as bladder agenesis and GT hypoplasia, which are derived from the aPCM with reduced Tbx4 and Tbx5 expression. Tbx4-expressing cells contribute to the mesenchyme of the bladder and GT by lineage analysis with Tbx4Cre R26R mice [50]. These results suggest that the aPCM is not formed in Bmp4 cKO mice. Hence, current observations indicate that the aPCM contains essential progenitors for pelvic/urogenital tissues. Normally, Bmp4 is expressed and BMP signaling is active in the aPCM during caudal body formation. Loss of pSMAD immunoreactivity in the aPCM region of Bmp4 cKO mice indicates that autocrine BMP4 action is required to form the aPCM. To investigate the role of BMP4 in the aPCM formation, we assessed apoptosis and cell proliferation by Tunel and EdU assay, respectively. Both conditions were not altered in Bmp4 cKO revealed a surprisingly wide range of abnormalities affecting the external genitalia as well as intra-pelvic organs and retroperitoneal organs. Current tissue lineage analyses suggest that Isl1-expressing cells are essential population of cells for the caudal body formation Figure 4. Isl1-expressing cells contribute to the aPCM. (A–C) Midsagittal sections of cloacal region at E10.5. The square indicates the aPCM (A). The Isl1-expressing cells contribute to the aPCM and URS (B, C). Arrows indicate the URS. u, URS; c,cloaca. doi:10.1371/journal.pone.0043453.g004 PLOS ONE | 5 September 2012 | Volume 7 | Issue 9 | e43453 A New Mouse Model of Sirenomelia Figure 5. Defective aPCM formation of Bmp4 cKO mice. (A) Bmp4 is expressed in the aPCM at E10.5. (B) Immunohistochemical analysis of pSMAD in the aPCM at E10.5. (C–J) Section in situ hybridization analysis with the aPCM and cloacal marker genes for wild type (C, E, G, I) and mutant embryos (D, F, H, J) at E10.5. (K–N) Immunohistochemical analysis of pSMAD in the aPCM of wild types (K) and mutant embryos (L) at E10.5. (M, N) High magnification images of square region in K and L. The squares in A–L indicate the aPCM. doi:10.1371/journal.pone.0043453.g005 An essentially important pathological feature of sirenomelia is leg fusion. The leg locates in the lateral body wall, which is supported by pelvic skeletons. Previous studies suggest abnormal formation of the leg is derived from the defective midline formation [52], [53]. The current phenotypes are associated with the aplasia of midline structure which is derived from the aPCM region. Although Shh KO mice show defective pelvic/urogenital formation, their mutants do not show the hindlimb fusion [14], [54]. 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